## Practice (Solutions)

### Tables

Complete each section to show your understanding for linear patterns.

The following tables represent linear patterns. The tables are created using *Desmos.com.*

Table 1 | Table 2 | Table 3 |

- Find the missing values in each table.
- Table 1: (3, 7) and (12,15)
- Table 2: (4, 9) and (21, -42)
- Table 3: (-2, 4) and (8, 24)

- Graph each table on a coordinate plane.
- Calculate the slope using the table.
- Table 1: change in \(y\) is 4 and change in \(x\) is 1, i.e. slope is 4
- Table 2: change in \(y\) is -3 and change in \(x\) is 1, i.e. slope is -3
- Table 3: change in \(y\) is 2 and change in \(x\) is 1, i.e. slope is 2

- Calculate the slope using the graph.
- Determine the point of the \(y\) intercept.
- Table 1: (0,-5)
- Table 2: (0,18)
- Table 3: (0,8)

- Write an equation to determine the \(y\)
*–*value given any \(x\)-value.- Table 1 equation: \(y = 4x -5\)
- Table 2 equation: \(y=21 – 3x\)
- Table 3 equation: \(y= 2x + 8\)

### Patterns

Given the growth pattern shown in Figure 2 and Figure 4.

- Draw Figure 3.
- Figure 3 has 3 rows of 6, so a row of 6 is added to Figure 2.

- Explain the growth pattern.
- 6 is added each time.

- Determine the number of squares in Figure 0.
- Figure 0 has 1 square.

- Write the equation to represent the number of squares for any figure.
- \(1 + 6n\), where \(n\) is the figure number.

- Using the context of growth patterns, explain why \(m\) represents the slope and \(b\) represents the \(y\)-intercept in the
*slope-intercept*formula \(y=mx+b\).- The slope is 6 since, 6 squares are added to create the next figure. To find the \(y\)-intercept we need to find the number of squares in Figure 0 which can be found by subtracting 6 squares from Figure 2 to find Figure 1, and another 6 squares from Figure 1 to find Figure 0, or 13-6-6 = 13-12 = 1. Therefore 1 is the \(y\)-intercept.

A given linear pattern has 10 squares in Step 3. The pattern grows by -4 squares every 2 steps.

- Create a table for this pattern.
- Calculate the slope to represent the growth for this pattern.
- Slope is -4

- Calculate the equation to calculate the number of squares for each step.
- \(y = 22 – 4x\)